In the previous article I looked at maths and formulas relevant to the Scope and Time of a project. Here, as a final article in the series, I would like to look at the maths applied to COST.
Every sector will have specific approaches to the financial aspects of a project, with specific economies, so I will have to be very generic here.
I would like to cover the maths under the following sections:
- Budget
- Financial ratios
- Investment appraisal
- Resources
- Earned value management.
I hope you will find the article interesting. I will be delighted to get feedback, especially from those with specific knowledge and experience.
Budget
The term ‘budget’ is used routinely in all organisations and it defines a particular sum of money that has been allocated for a particular item, purpose, or event over a specific or fixed period of time. In relation to project management, the term has a similar meaning, representing “an approved estimate for either the entire project or for a particular scheduled activity or work structure breakdown component“. It is one of the sides of the “devil’s triangle” of project management.
A budget is prepared by following simple arithmetic. There are various approaches to budgeting, but the simplest to understand is the one that considers the breaking down of the project in workstreams, phases, activities or tasks (Work Breakdown) and the assignment to them of the anticipated resource and cost requirements. These costs will be under various categories, such as: salaries, travel expenditure, training costs, materials, research and professional fees, services, capital expenditure, taxes, contingencies, etc.
The interesting part is the Forecasting. Once the Project Manager has build up the estimated total budget, she/he will have to look at the accurateness of the budget and will have to consider worst-case and best-case scenarios. These scenarios may include evaluation of risks, like fluctuation in exchange ratios, inflation and other context risks. The Monte Carlo simulation provides a means of evaluating the effect of uncertainty in a wide range of simulations, using random numbers to parameters from probability distributions (see previous article).
You may want to apply a Three-Point Estimate, where you average the three possible selected scenarios, the optimistic, pessimistic and most-likely. (See also the trade-off exercise at the end of the article).
Financial ratios
I am vague here, as this is not my area of expertise.
In assessing costs, it may be appropriate to review the financial situation of key contractors or suppliers, as to assess their strengths or weaknesses. This may be particularly relevant for major programmes or for selecting major contractors or service providers for a bid in a project.
There is simple arithmetic applied in the form of Financial Ratios or Accounting Ratios. These are ratios showing relative magnitude of selected numerical parameters and indicators taken from an organisation’s financial statement. This is something of competence for your colleagues in the Finance department.
Investment appraisal
This is the financial assessment of projects to check affordability and feasibility. It may be used as a criteria for selecting amongst various potential projects the one that might offer the best return.
The arithmetic underpinning the Investment Appraisal is surprisingly simple and the challenges are with the appropriate use and interpretation, in relation to the organisations’ objectives and risk appetite. The four main techniques I found are:
- Average rate of return (ARR)
- Payback period (PP)
- Net present value (NPV) and
- Internal rat of return (IRR).
If you have a specific interest you may check this article.
Resources
The concept of Full-Time Equivalent (FTE) is very important in project management. FTE is a unit of time defined to measure the workload or availability or capacity of an employee. It refers to the number of hours worked by a single employee in a week. If we assume the annual FTE count to be 2,080 hours, this breaks down into 8 hours per day, 5 days a week. Although the maths underpinning the concept is rather simple, I am sure many of you have been challenged by the concept.
The FTE calculation is used in project management (and resource management, specifically) to make decisions about staffing decisions. For example, if you have a project that is estimated to require 640 hours of work, and assuming a 8 hours working day, you can determine your personnel requirements using the following FTE equation:
640 hs = 8 hs x (# full-time employees) x (# days worked).
Dividing 640 by 8 you get 80. There are several ways to break down that 80, depending on your needs or your organisational layout. As an example, you could choose to assign 4 full-time employees to work on the project for 20 days. If the work has to be completed in 10 days, you know that you have to assign 8 full-time workers. You can adjust and diversify the calculations based on the project’s scope and requirements, scaling up or down as necessary, including part-time employees.
Those working with Microsoft Project might have been challenged with the calculation between %Units, Duration and Work. It is still very simple arithmetic. Units% means the level of utilisation of a Work Resource, with 100% meaning full time on the assigned task. If a task duration is one week, this means 40 hours. A Units% at 50% means 20 hours. The Duration will be a result of the calculation of Units% converted to an equivalent number of work hours, which are converted in working weeks by MS-Project using the underlying working calendar. According to the manual, MS-Project has a specific sequence for the calculations, summarised in the table below:
If you enter the Units% and the Duration, the Work hours are calculated, etc. If you assign a resource at 10% and then you set the Work hours to, say, 10 hours, MS- Project will calculate a Duration of 2.5 weeks, as 40 hs x 10% = 4 hours worked per week, 10/4= 2.5 week to complete the 10 hours. I hope this makes sense?
Earned value management
Earned Value Management (EVM) is a project management technique that measures project progress objectively. EVM combines measurements of scope performance, schedule performance and cost performance within a single integrated methodology. It somehow encompasses elements of scheduling that were covered in the previous article.
EVM provides an early warning of performance problems, clearly working better for traditional “waterfall” projects.
The maths underpinning EVM is simple arithmetic and it will utilise parameters for which the acronyms are quite important to remember (especially for those who are taking an exam for a PM certification) – check this link, for reference. You may need to remember:
- EV = Earned Value
- PV = Planned Value
- AC = Actual Cost
- CV = Cost Variance
- SV = Schedule Variance
- CPI = Cost Performance Index
- SPI = Schedule Performance Index
- BAC = Budget at Completion
- ETC = Estimate to Complete
- EAC = Estimate at Completion.
It will be about relating Costs (either budgeted or actual) to Work (either scheduled or completed).
An interesting consideration is the time-costs trade offs that can be incorporated in the PERT calculation (see article on TIME for PERT). Using the example of the house build presented in the previous article, we can add costs, as regular, or the additional ones (“crash” costs) that can be added to reduce the duration of the tasks. For example:
| Task ID | Optimistic time | Mode | Pessimistic time | Crash time | Regular costs | Crash costs |
| A | 1 week | 2 weeks | 3 weeks | 1 week | 2000 | 3000 |
| B | 5 weeks | 7 weeks | 9 weeks | 5 weeks | 7000 | 9000 |
| C | 3 weeks | 4 weeks | 5 weeks | 3 weeks | 4000 | 5000 |
| D | 2 weeks | 3 weeks | 4 weeks | 2 weeks | 3000 | 4000 |
| E | 1 week | 2 weeks | 3 weeks | 1 week | 2000 | 3000 |
For Tasks A, for example, the duration can be reduced to 1 week by increasing the cost to 3000.
By reducing the duration of the tasks on the critical path, tasks that were previously non-critical will become critical. Time reductions may become progressively expensive. There will be a number of iterations to do in which total crash costs and estimated new times of completion for the project will be worked out. These can be plotted to work out the optimal crash that minimises also the costs. I will stop here as this is a rather unfamiliar territory for me!
What about Agile projects?
Well, some of the formulas above would still apply – see this link related to PMP-ACP for guidance. It seems that while Earned Value Management is a broad and important concept in traditional project management, it has been downsized and adapted for use in Agile projects.
As indicated in this article, it seems that estimating costs in an Agile environment requires a more iterative, integrated and collaborative approach than in traditional programs. The article will give a more detailed explanation, but I would welcome feedback from those readers who have more experience with Agile.
In this article I provided an overview of the maths and formulas that in my opinion would help in the project COST definition and control. This is the last article in the series. I hope it was interesting and please do not hesitate to contact me for any comments and constructive feedback.
Marco Bottacini, Senior Portfolio Manager, GALVmed
The views and opinions expressed in this blog are those of the author and do not necessarily reflect the views and opinion of GALVmed.
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